Question

1) What is the reactance of an inductor with an inductance of 2.60 H at a frequency of 78.0 Hz ?

2) What is the inductance of an inductor whose reactance is 12.8 Ω at a frequency of 78.0 Hz ?

3) What is the reactance of a capacitor with a capacitance of 3.78×10⁻⁶ F at a frequency of 78.0 Hz ?

4) What is the capacitance of a capacitor whose reactance is 130 Ω at a frequency of 78.0 Hz ?

Answer 1

here,

1)

the inductance , L = 2.6 H

frequency , f = 78 Hz

the reactance of inductor , Xl = 2 *pi * f * L

Xl = 2 *pi * 78 * 2.6 ohm

Xl = 1273.6 ohm

2)

let the inductance be L

frequency , f = 78 Hz

the reactance of inductor , Xl = 2 *pi * f * L

12.8 = 2 *pi * 78 * L

L = 0.026 H

the inductance is 0.026 H

3)

capacitance , C = 3.78 * 10^-6 F

frequency , f = 78 Hz

the capacitive reactance , Xc = 1/(2*pi*f*C)

Xc = 1/(2*pi*78*3.78 * 10^-6)

Xc = 540 ohm

4)

frequency , f = 78 Hz

the capacitive reactance , Xc = 1/(2*pi*f*C)

130 = 1/(2*pi*78* C)

solving for C

C = 1.57 * 10^-5 F